Statistical Processing Methods used in Abnormal Situation Detection

ABSTRACT

Detection of one or more abnormal situations is performed using various statistical measures, such as a mean, a median, a standard deviation, etc. of one or more process parameters or variable measurements made by statistical process monitoring blocks within a plant. This detection is enhanced in various cases by using specialized data filters and data processing techniques, which are designed to be computationally simple and therefore are able to be applied to data collected at a high sampling rate in a field device having limited processing power. The enhanced data or measurements may be used to provided better or more accurate statistical measures of the data, may be used to trim the data to remove outliers from this data, may be used to fit this data to non-linear functions, or may be use to quickly detect the occurrence of various abnormal situations within specific plant equipment, such as distillation columns and fluid catalytic crackers.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.60/668,243 entitled “Process Diagnostics,” which was filed on Apr. 4,2005 and which is hereby expressly incorporated by reference herein inits entirety for all purposes.

FIELD OF THE DISCLOSURE

This patent relates generally to performing diagnostics and maintenancein a process plant and, more particularly, to providing diagnosticcapabilities within a process plant in a manner that reduces or preventsabnormal situations within the process plant.

BACKGROUND

Process control systems, like those used in chemical, petroleum or otherprocesses, typically include one or more centralized or decentralizedprocess controllers communicatively coupled to at least one host oroperator workstation and to one or more process control andinstrumentation devices such as, for example, field devices, via analog,digital or combined analog/digital buses. Field devices, which may be,for example, valves, valve positioners, switches, transmitters, andsensors (e.g., temperature, pressure, and flow rate sensors), arelocated within the process plant environment, and perform functionswithin the process such as opening or closing valves, measuring processparameters, increasing or decreasing fluid flow, etc. Smart fielddevices such as field devices conforming to the well-known FOUNDATION™Fieldbus (hereinafter “Fieldbus”) protocol or the HART® protocol mayalso perform control calculations, alarming functions, and other controlfunctions commonly implemented within the process controller.

The process controllers, which are typically located within the processplant environment, receive signals indicative of process measurements orprocess variables made by or associated with the field devices and/orother information pertaining to the field devices, and executecontroller applications. The controller applications implement, forexample, different control modules that make process control decisions,generate control signals based on the received information, andcoordinate with the control modules or blocks being performed in thefield devices such as HART and Fieldbus field devices. The controlmodules in the process controllers send the control signals over thecommunication lines or signal paths to the field devices, to therebycontrol the operation of the process.

Information from the field devices and the process controllers istypically made available to one or more other hardware devices such as,for example, operator workstations, maintenance workstations, personalcomputers, handheld devices, data historians, report generators,centralized databases, etc. to enable an operator or a maintenanceperson to perform desired functions with respect to the process such as,for example, changing settings of the process control routine, modifyingthe operation of the control modules within the process controllers orthe smart field devices, viewing the current state of the process or ofparticular devices within the process plant, viewing alarms generated byfield devices and process controllers, simulating the operation of theprocess for the purpose of training personnel or testing the processcontrol software, diagnosing problems or hardware failures within theprocess plant, etc.

While a typical process plant has many process control andinstrumentation devices such as valves, transmitters, sensors, etc.connected to one or more process controllers, there are many othersupporting devices that are also necessary for or related to processoperation. These additional devices include, for example, power supplyequipment, power generation and distribution equipment, rotatingequipment such as turbines, motors, etc., which are located at numerousplaces in a typical plant. While this additional equipment does notnecessarily create or use process variables and, in many instances, isnot controlled or even coupled to a process controller for the purposeof affecting the process operation, this equipment is neverthelessimportant to, and ultimately necessary for proper operation of theprocess.

As is known, problems frequently arise within a process plantenvironment, especially a process plant having a large number of fielddevices and supporting equipment. These problems may take the form ofbroken or malfunctioning devices, plugged fluid lines or pipes, logicelements, such as software routines, being improperly configured orbeing in improper modes, process control loops being improperly tuned,one or more failures in communications between devices within theprocess plant, etc. These and other problems, while numerous in nature,generally result in the process operating in an abnormal state (i.e.,the process plant being in an abnormal situation) which is usuallyassociated with suboptimal performance of the process plant. Manydiagnostic tools and applications have been developed to detect anddetermine the cause of problems within a process plant and to assist anoperator or a maintenance person to diagnose and correct the problems,once the problems have occurred and been detected. For example, operatorworkstations, which are typically connected to the process controllersthrough communication connections such as a direct or a wireless bus, anEthernet, a modem, a phone line, and the like, have processors andmemories that are adapted to run software or firmware, such as theDeltaV™ and Ovation control systems, sold by Emerson Process Management,wherein the software includes numerous control module and control loopdiagnostic tools. Likewise, maintenance workstations, which may beconnected to the process control devices, such as field devices, via thesame communication connections as the controller applications, or viadifferent communication connections, such as OPC connections, handheldconnections, etc., typically include one or more applications designedto view maintenance alarms and alerts generated by field devices withinthe process plant, to test devices within the process plant and toperform maintenance activities on the field devices and other deviceswithin the process plant. Similar diagnostic applications have beendeveloped to diagnose problems within the supporting equipment withinthe process plant.

Thus, for example, the Asset Management Solutions (AMS) application (atleast partially disclosed in U.S. Pat. No. 5,960,214 entitled“Integrated Communication Network for use in a Field Device ManagementSystem”) sold by Emerson Process Management, enables communication withand stores data pertaining to field devices to ascertain and track theoperating state of the field devices. In some instances, the AMSapplication may be used to communicate with a field device to changeparameters within the field device, to cause the field device to runapplications on itself such as, for example, self-calibration routinesor self-diagnostic routines, to obtain information about the status orhealth of the field device, etc. This information may include, forexample, status information (e.g., whether an alarm or other similarevent has occurred), device configuration information (e.g., the mannerin which the field device is currently or may be configured and the typeof measuring units used by the field device), device parameters (e.g.,the field device range values and other parameters), etc. Of course,this information may be used by a maintenance person to monitor,maintain, and/or diagnose problems with field devices.

Similarly, many process plants include equipment monitoring anddiagnostic applications such as, for example, RBMware provided by CSISystems, or any other known applications used to monitor, diagnose, andoptimize the operating state of various rotating equipment. Maintenancepersonnel usually use these applications to maintain and oversee theperformance of rotating equipment in the plant, to determine problemswith the rotating equipment, and to determine when and if the rotatingequipment must be repaired or replaced. Similarly, many process plantsinclude power control and diagnostic applications such as those providedby, for example, the Liebert and ASCO companies, to control and maintainthe power generation and distribution equipment. It is also known to runcontrol optimization applications such as, for example, real-timeoptimizers (RTO+), within a process plant to optimize the controlactivities of the process plant. Such optimization applicationstypically use complex algorithms and/or models of the process plant topredict how inputs may be changed to optimize operation of the processplant with respect to some desired optimization variable such as, forexample, profit.

These and other diagnostic and optimization applications are typicallyimplemented on a system-wide basis in one or more of the operator ormaintenance workstations, and may provide preconfigured displays to theoperator or maintenance personnel regarding the operating state of theprocess plant, or the devices and equipment within the process plant.Typical displays include alarming displays that receive alarms generatedby the process controllers or other devices within the process plant,control displays indicating the operating state of the processcontrollers and other devices within the process plant, maintenancedisplays indicating the operating state of the devices within theprocess plant, etc. Likewise, these and other diagnostic applicationsmay enable an operator or a maintenance person to retune a control loopor to reset other control parameters, to run a test on one or more fielddevices to determine the current status of those field devices, tocalibrate field devices or other equipment, or to perform other problemdetection and correction activities on devices and equipment within theprocess plant.

While these various applications and tools are very helpful inidentifying and correcting problems within a process plant, thesediagnostic applications are generally configured to be used only after aproblem has already occurred within a process plant and, therefore,after an abnormal situation already exists within the plant.Unfortunately, an abnormal situation may exist for some time before itis detected, identified and corrected using these tools, resulting inthe suboptimal performance of the process plant for the period of timeduring which the problem is detected, identified and corrected. In manycases, a control operator will first detect that some problem existsbased on alarms, alerts or poor performance of the process plant. Theoperator will then notify the maintenance personnel of the potentialproblem. The maintenance personnel may or may not detect an actualproblem and may need further prompting before actually running tests orother diagnostic applications, or performing other activities needed toidentify the actual problem. Once the problem is identified, themaintenance personnel may need to order parts and schedule a maintenanceprocedure, all of which may result in a significant period of timebetween the occurrence of a problem and the correction of that problem,during which time the process plant runs in an abnormal situationgenerally associated with the sub-optimal operation of the plant.

Additionally, many process plants can experience an abnormal situationwhich results in significant costs or damage within the plant in arelatively short amount of time. For example, some abnormal situationscan cause significant damage to equipment, the loss of raw materials, orsignificant unexpected downtime within the process plant if theseabnormal situations exist for even a short amount of time. Thus, merelydetecting a problem within the plant after the problem has occurred, nomatter how quickly the problem is corrected, may still result insignificant loss or damage within the process plant. As a result, it isdesirable to try to prevent abnormal situations from arising in thefirst place, instead of simply trying to react to and correct problemswithin the process plant after an abnormal situation arises.

There is currently one technique that may be used to collect data thatenables a user to predict the occurrence of certain abnormal situationswithin a process plant before these abnormal situations actually ariseor shortly after they arise, with the purpose of taking steps to preventthe predicted abnormal situation or to correct the abnormal situationbefore any significant loss within the process plant takes place. Thisprocedure is disclosed in U.S. patent application Ser. No. 09/972,078,entitled “Root Cause Diagnostics” (based in part on U.S. patentapplication Ser. No. 08/623,569, now U.S. Pat. No. 6,017,143). Theentire disclosures of both of these applications/patents are herebyincorporated by reference herein. Generally speaking, this techniqueplaces statistical data collection and processing blocks or statisticalprocessing monitoring (SPM) blocks, in each of a number of devices, suchas field devices, within a process plant. The statistical datacollection and processing blocks collect, for example, process variabledata and determine certain statistical measures associated with thecollected data, such as a mean, a median, a standard deviation, etc.These statistical measures may then sent to a user interface or otherprocessing device and analyzed to recognize patterns suggesting theactual or future occurrence of a known abnormal situation. Once aparticular suspected abnormal situation is detected, steps may be takento correct the underlying problem, thereby avoiding the abnormalsituation in the first place or correcting the abnormal situationquickly. However, the collection and analysis of this data may be timeconsuming and tedious for a typical maintenance operator, especially inprocess plants having a large number of field devices collecting thisstatistical data. Still further, while a maintenance person may be ableto collect the statistical data, this person may not know how to bestanalyze or view the data or to determine what, if any, future abnormalsituation may be suggested by the data.

SUMMARY

Detection or prediction of one or more abnormal situations is performedusing various statistical measures, such as a mean, median, standarddeviation, etc. of process parameters or variable measurementsdetermined by statistical process monitoring (SPM) blocks within aplant. This detection is enhanced in various cases by the use ofspecialized data filters and data processing techniques, which aredesigned to be computationally simple and therefore are able to beapplied to data collected at a high sampling rate in a field devicehaving limited processing power. The enhanced data or measurements maybe used to provided better or more accurate statistical measures of theprocess variable or process parameter, may be used to trim the data toremove outliers from this data, may be used to fit this data tonon-linear functions, or may be use to quickly detect the occurrence ofvarious abnormal situations within specific plant equipment, such asdistillation columns and refinery catalytic crackers. While thestatistical data collection and processing and abnormal situationdetection may be performed within a user interface device or othermaintenance device within a process plant, these methods may also andadvantageously be used in the devices, such as field devices likevalves, transmitters, etc. which collect the data in the first place,thereby removing the processing burden from the centralized userinterface device as well as the conmunication overhead associated withsending the statistical data from the field devices to the userinterface device.

The methods described herein can be applied in many different scenarioswithin a process plant on many different types of data, to detectwhether one or more abnormal situations exist or may be developingwithin a plant. For example, the statistical data may comprisestatistical data generated based on pressure, level, flow, position andtemperature variables sensed by one or more pressure, level, flow,position and temperature sensors associated with, for example, adistillation column or a refinery catalytic cracker unit. Of course, ifan abnormal situation is detected, an indicator of the abnormalsituation may be generated and the indicator may be used, for example,to notify an operator or maintenance personnel or to affect control ofplant equipment.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an exemplary block diagram of a process plant having adistributed control and maintenance network including one or moreoperator and maintenance workstations, controllers, field devices andsupporting equipment;

FIG. 2 is an exemplary block diagram of a portion of the process plantof FIG. 1, illustrating communication interconnections between variouscomponents of an abnormal situation prevention system located withindifferent elements of the process plant, including the use ofstatistical process monitoring (SPM) blocks;

FIG. 3 is a block diagram of an example SPM block;

FIG. 4 is a display illustrating the configuration of a set ofstatistical process monitoring blocks within a device of the processplant of FIG. 1 or 2;

FIG. 5 is a block diagram of an example SPM module that uses multipleSPM blocks and a data processing block to perform signal processing onraw data to produce enhanced SPM statistics;

FIG. 6 is a block diagram of a first example data processing block ofFIG. 5 that implements one of multiple different types of filters;

FIG. 7 is a block diagram of a second example data processing block ofFIG. 5 that includes data trimming blocks and that implements one ormore different types of filters to produce filtered and trimmed data;

FIG. 8 illustrates the transfer function of a known 16^(th) order FIRhigh pass filter.

FIG. 9 illustrates a transfer function of a difference filter that maybe used to filter received process data in an SPM module;

FIG. 10 illustrates a set of raw pressure data including process noiseand transients to which the filter of FIG. 9 is to be applied;

FIG. 11 illustrates a set of filtered data after application of thefilter of FIG. 9 on the pressure data of FIG. 10;

FIG. 12 illustrates a plot of a typical pressure signal in the timedomain;

FIG. 13 illustrates a frequency domain representation of the pressuresignal of FIG. 12 after the application of a Fast Fourier Transform;

FIG. 14 is a block diagram of a typical distillation column used inrefineries and chemical plants;

FIG. 15 is a block diagram illustrating various trays of thefractionator of the distillation column of FIG. 14; and

FIG. 16 is a block diagram of a typical fluid catalytic cracker used ina refinery.

DETAILED DESCRIPTION

Referring now to FIG. 1, an example process plant 10 in which anabnormal situation prevention system may be implemented includes anumber of control and maintenance systems interconnected together withsupporting equipment via one or more communication networks. Inparticular, the process plant 10 of FIG. 1 includes one or more processcontrol systems 12 and 14. The process control system 12 may be atraditional process control system such as a PROVOX or RS3 system or anyother control system which includes an operator interface 12A coupled toa controller 12B and to input/output (I/O) cards 12C which, in turn, arecoupled to various field devices such as analog and Highway AddressableRemote Transmitter (HART) field devices 15. The process control system14, which may be a distributed process control system, includes one ormore operator interfaces 14A coupled to one or more distributedcontrollers 14B via a bus, such as an Ethernet bus. The controllers 144Bmay be, for example, DeltaV™ controllers sold by Emerson ProcessManagement of Austin, Tex. or any other desired type of controllers. Thecontrollers 14B are connected via I/O devices to one or more fielddevices 16, such as for example, HART or Fieldbus field devices or anyother smart or non-smart field devices including, for example, thosethat use any of the PROFIBUS®, WORLDFIP®, Device-Net®, AS-Interface andCAN protocols. As is known, the field devices 16 may provide analog ordigital information to the controllers 14B related to process variablesas well as to other device information. The operator interfaces 14A maystore and execute tools available to the process control operator forcontrolling the operation of the process including, for example, controloptimizers, diagnostic experts, neural networks, tuners, etc.

Still further, maintenance systems, such as computers executing the AMSapplication or any other device monitoring and communicationapplications may be connected to the process control systems 12 and 14or to the individual devices therein to perform maintenance andmonitoring activities. For example, a maintenance computer 18 may beconnected to the controller 12B and/or to the devices 15 via any desiredcommunication lines or networks (including wireless or handheld devicenetworks) to communicate with and, in some instances, to reconfigure orto perform other maintenance activities on the devices 15. Similarly,maintenance applications such as the AMS application may be installed inand executed by one or more of the user interfaces 14A associated withthe distributed process control system 14 to perform maintenance andmonitoring functions, including data collection related to the operatingstatus of the devices 16.

The process plant 10 also includes various rotating equipment 20, suchas turbines, motors, etc. which are connected to a maintenance computer22 via some permanent or temporary communication link (such as a bus, awireless communication system or hand held devices which are connectedto the equipment 20 to take readings and are then removed). Themaintenance computer 22 may store and execute known monitoring anddiagnostic applications 23 provided by, for example, CSI (an EmersonProcess Management Company) or other any other known applications usedto diagnose, monitor and optimize the operating state of the rotatingequipment 20. Maintenance personnel usually use the applications 23 tomaintain and oversee the performance of rotating equipment 20 in theplant 10, to determine problems with the rotating equipment 20 and todetermine when and if the rotating equipment 20 must be repaired orreplaced. In some cases, outside consultants or service organizationsmay temporarily acquire or measure data pertaining to the equipment 20and use this data to perform analyses for the equipment 20 to detectproblems, poor performance or other issues effecting the equipment 20.In these cases, the computers running the analyses may not be connectedto the rest of the system 10 via any communication line or may beconnected only temporarily.

Similarly, a power generation and distribution system 24 having powergenerating and distribution equipment 25 associated with the plant 10 isconnected via, for example, a bus, to another computer 26 which runs andoversees the operation of the power generating and distributionequipment 25 within the plant 10. The computer 26 may execute knownpower control and diagnostics applications 27 such a as those providedby, for example, Liebert and ASCO or other companies to control andmaintain the power generation and distribution equipment 25. Again, inmany cases, outside consultants or service organizations may use serviceapplications that temporarily acquire or measure data pertaining to theequipment 25 and use this data to perform analyses for the equipment 25to detect problems, poor performance or other issues effecting theequipment 25. In these cases, the computers (such as the computer 26)running the analyses may not be connected to the rest of the system 10via any communication line or may be connected only temporarily.

As illustrated in FIG. 1, a computer system 30 implements at least aportion of an abnormal situation prevention system 35, and inparticular, the computer system 30 stores and implements a configurationand data collection application 38, a viewing or interface application40, which may include statistical collection and processing blocks, anda rules engine development and execution application 42 and,additionally, stores a statistical process monitoring database 43 thatstores statistical data generated within certain devices within theprocess, such as statistical measures of various process parameters.Generally speaking, the configuration and data collection application 38configures and communicates with each of a number of statistical datacollection and analysis blocks (not shown in FIG. 1) located in thefield devices 15, 16, the controllers 12B, 14B, the rotating equipment20 or its supporting computer 22, the power generation equipment 25 orits supporting computer 26 and any other desired devices and equipmentwithin the process plant 10, to thereby collect statistical data (or insome cases, actual raw process variable data) from each of these blockswith which to perform abnormal situation detection. The configurationand data collection application 38 may be communicatively connected viaa hardwired bus 45 to each of the computers or devices within the plant10 or, alternatively, may be connected via any other desiredcommunication connection including, for example, wireless connections,dedicated connections which use OPC, intermittent connections, such asones which rely on handheld devices to collect data, etc.

Likewise, the application 38 may obtain data pertaining to the fielddevices and equipment within the process plant 10 via a LAN or a publicconnection, such as the Internet, a telephone connection, etc.(illustrated in FIG. 1 as an Internet connection 46) with such databeing collected by, for example, a third party service provider.Further, the application 38 may be communicatively coupled tocomputers/devices in the plant 10 via a variety of techniques and/orprotocols including, for example, Ethernet, Modbus, HTML, XML,proprietary techniques/protocols, etc. Thus, although particularexamples using OPC to communicatively couple the application 38 tocomputers/devices in the plant 10 are described herein, one of ordinaryskill in the art will recognize that a variety of other methods ofcoupling the application 38 to computers/devices in the plant 10 can beused as well. The application 38 may generally store the collected datain the database 43.

Once the statistical data (or process variable data) is collected, theviewing application 40 may be used to process this data and/or todisplay the collected or processed statistical data (e.g., as stored inthe database 43) in different manners to enable a user, such as amaintenance person, to better be able to determine the existence of orthe predicted future existence of an abnormal situation and to takepreemptive or actual corrective actions. The rules engine developmentand execution application 42 may use one or more rules stored therein toanalyze the collected data to determine the existence of, or to predictthe future existence of an abnormal situation within the process plant10. Additionally, the rules engine development and execution application42 may enable an operator or other user to create additional rules to beimplemented by a rules engine to detect or predict abnormal situations.It is appreciated that the detection of an abnormal situation asdescribed herein encompasses the prediction of a future occurrence of anabnormal situation.

FIG. 2 illustrates a portion 50 of the example process plant 10 of FIG.1 for the purpose of describing one manner in which statistical datacollection and processing and in some cases abnormal situation detectionmay be performed by components associated with the abnormal situationprevention system 35 including blocks located within field devices.While FIG. 2 illustrates communications between the abnormal situationprevention system applications 38, 40 and 42 and the database 43 and oneor more data collection and processing blocks within HART and Fieldbusfield devices, it will be understood that similar communications canoccur between the abnormal situation prevention system applications 38,40 and 42 and other devices and equipment within the process plant 10,including any of the devices and equipment illustrated in FIG. 1.

The portion 50 of the process plant 10 illustrated in FIG. 2 includes adistributed process control system 54 having one or more processcontrollers 60 connected to one or more field devices 64 and 66 viainput/output (I/O) cards or devices 68 and 70, which may be any desiredtypes of I/O devices conforming to any desired communication orcontroller protocol. The field devices 64 are illustrated as HART fielddevices and the field devices 66 are illustrated as Fieldbus fielddevices, although these field devices could use any other desiredcommunication protocols. Additionally, the field devices 64 and 66 maybe any types of devices such as, for example, sensors, valves,transmitters, positioners, etc., and may conform to any desired open,proprietary or other communication or programming protocol, it beingunderstood that the I/O devices 68 and 70 must be compatible with thedesired protocol used by the field devices 64 and 66.

In any event, one or more user interfaces or computers 72 and 74 (whichmay be any types of personal computers, workstations, etc.) accessibleby plant personnel such as configuration engineers, process controloperators, maintenance personnel, plant managers, supervisors, etc. arecoupled to the process controllers 60 via a communication line or bus 76which may be implemented using any desired hardwired or wirelesscommunication structure, and using any desired or suitable communicationprotocol such as, for example, an Ethernet protocol. In addition, adatabase 78 may be connected to the communication bus 76 to operate as adata historian that collects and stores configuration information aswell as on-line process variable data, parameter data, status data, andother data associated with the process controllers 60 and field devices64 and 66 within the process plant 10. Thus, the database 78 may operateas a configuration database to store the current configuration,including process configuration modules, as well as controlconfiguration information for the process control system 54 asdownloaded to and stored within the process controllers 60 and the fielddevices 64 and 66. Likewise, the database 78 may store historicalabnormal situation prevention data, including statistical data collectedand/or generated by the field devices 64 and 66 within the process plant10 or statistical data determined from process variables collected bythe field devices 64 and 66.

While the process controllers 60, I/O devices 68 and 70, and fielddevices 64 and 66 are typically located down within and distributedthroughout the sometimes harsh plant environment, the workstations 72and 74, and the database 78 are usually located in control rooms,maintenance rooms or other less harsh environments easily accessible byoperators, maintenance personnel, etc.

Generally speaking, the process controllers 60 store and execute one ormore controller applications that implement control strategies using anumber of different, independently executed, control modules or blocks.The control modules may each be made up of what are commonly referred toas function blocks, wherein each function block is a part or asubroutine of an overall control routine and operates in conjunctionwith other function blocks (via communications called links) toimplement process control loops within the process plant 10. As is wellknown, function blocks, which may be objects in an object-orientedprogramming protocol, typically perform one of an input function, suchas that associated with a transmitter, a sensor or other processparameter measurement device, a control function, such as thatassociated with a control routine that performs PID, fuzzy logic, etc.control, or an output function, which controls the operation of somedevice, such as a valve, to perform some physical function within theprocess plant 10. Of course, hybrid and other types of complex functionblocks exist, such as model predictive controllers (MPCs), optimizers,etc. It is to be understood that while the Fieldbus protocol and theDeltaV™ system protocol use control modules and function blocks designedand implemented in an object-oriented programming protocol, the controlmodules may be designed using any desired control programming schemeincluding, for example, sequential function blocks, ladder logic, etc.,and are not limited to being designed using function blocks or any otherparticular programming technique.

As illustrated in FIG. 2, the maintenance workstation 74 includes aprocessor 74A, a memory 74B and a display device 74C. The memory 74Bstores the abnormal situation prevention applications 38, 40 and 42discussed with respect to FIG. 1 in a manner that these applications canbe implemented on the processor 74A to provide information to a user viathe display 74C (or any other display device, such as a printer).

Additionally, as shown in FIG. 2, some (and potentially all) of thefield devices 64 and 66 include data collection and processing blocks 80and 82. While, the blocks 80 and 82 are described with respect to FIG. 2as being advanced diagnostics blocks (ADBs), which are known FoundationFieldbus function blocks that can be added to Fieldbus devices tocollect and process statistical data within Fieldbus devices, for thepurpose of this discussion, the blocks 80 and 82 could be or couldinclude any other type of block or module located within a processdevice that collects device data and calculates or determines one ormore statistical measures or parameters for that data, whether or notthese blocks are located in Fieldbus devices or conform to the Fieldbusprotocol. While the blocks 80 and 82 of FIG. 2 are illustrated as beinglocated in one of the devices 64 and in one of the devices 66, these orsimilar blocks could be located in any number of the field devices 64and 66, could be located in other devices, such as the controller 60,the I/O devices 68, 70, in an intermediate device that is located withinthe plant and that communicates with multiple sensors or transmittersand with the controller 60, or any of the devices illustrated in FIG. 1.Additionally, the blocks 80 and 82 could be in any subset of the devices64 and 66.

Generally speaking, the blocks 80 and 82 or sub-elements of theseblocks, collect data, such a process variable data, within the device inwhich they are located and perform statistical processing or analysis onthe data for any number of reasons. For example, the block 80, which isillustrated as being associated with a valve, may have a stuck valvedetection routine which analyzes the valve process variable data todetermine if the valve is in a stuck condition. In addition, the block80 includes a set of four statistical process monitoring (SPM) blocks orunits SPM1-SPM4 which may collect process variable or other data withinthe valve and perform one or more statistical calculations on thecollected data to determine, for example, a mean, a median, a standarddeviation, a root-mean-square (RMS), a rate of change, a range, aminimum, a maximum, etc. of the collected data and/or to detect eventssuch as drift, bias, noise, spikes, etc., in the collected data. Neitherthe specific statistical data generated, nor the method in which it isgenerated is critical. Thus, different types of statistical data can begenerated in addition to, or instead of, the specific types describedabove. Additionally, a variety of techniques, including knowntechniques, can be used to generate such data. The term statisticalprocess monitoring (SPM) block is used herein to describe functionalitythat performs statistical process monitoring on at least one processvariable or other process parameter, and may be performed by any desiredsoftware, firmware or hardware within the device or even outside of adevice for which data is collected. It will be understood that, becausethe SPMs are generally located in the devices where the device data iscollected, the SPMs can acquire quantitatively and qualitatively moreaccurate process variable data. As a result, the SPM blocks aregenerally capable of determining better statistical calculations withrespect to the collected process variable data than a block locatedoutside of the device in which the process variable data is collected.

As another example, the block 82 of FIG. 2, which is illustrated asbeing associated with a transmitter, may have a plugged line detectionunit that analyzes the process variable data collected by thetransmitter to determine if a line within the plant is plugged. Inaddition, the block 82 includes a set of four SPM blocks or unitsSPM1-SPM4 which may collect process variable or other data within thetransmitter and perform one or more statistical calculations on thecollected data to determine, for example, a mean, a median, a standarddeviation, etc. of the collected data. If desired, the underlyingoperation of the blocks 80 and 82 may be performed or implemented asdescribed in U.S. Pat. No. 6,017,143 referred to above. While the blocks80 and 82 are illustrated as including four SPM blocks each, the blocks80 and 82 could have any other number of SPM blocks therein forcollecting data and determining statistical measures associated withthat data. Likewise, while the blocks 80 and 82 are illustrated asincluding detection software for detecting particular conditions withinthe plant 10, they need not have such detection software or couldinclude detection software for detecting other conditions within theplant as described below. Still further, while the SPM blocks discussedherein are illustrated as being sub-elements of ADBs, they may insteadbe stand-alone blocks located within a device. Also, while the SPMblocks discussed herein may be known Foundation Fieldbus SPM blocks, theterm statistical process monitoring (SPM) block is used herein to referto any type of block or element that collects data, such as processvariable data, and performs some statistical processing on this data todetermine a statistical measure, such as a mean, a standard deviation,etc. As a result, this term is intended to cover software or firmware orother elements that perform this function, whether these elements are inthe form of function blocks, or other types of blocks, programs,routines or elements and whether or not these elements conform to theFoundation Fieldbus protocol, or some other protocol, such as PROFIBUS,WORLDFIP, Device-Net, AS-Interface, HART, CAN, etc., protocols.

FIG. 3 illustrates a block diagram of an SPM block 90 (which could beany of the SPM blocks in the blocks 80 and 82 of FIG. 2) which acceptsraw data on an input 92 and operates to calculate various statisticalmeasures of that data, including a Mean, an RMS value, and one or morestandard deviations. For a given set of raw input data, the block 90 mayalso determine a minimum value (Min), a maximum value (Max) and a range.If desired, this block may calculate specific points within the data,such as the Q25, Q50 and Q75 points and may perform outliner removalbased on the distributions. Of course this statistical processing can beperformed using any desired or known processing techniques.

Referring again to FIG. 2, in one embodiment, each SPM block within theADBs 80 and 82 can be either active or inactive. An active SPM block isone that is currently monitoring a process variable (or other processparameter) while an inactive SPM block is one that is not currentlymonitoring a process variable. Generally speaking, SPM blocks are, bydefault, inactive and, therefore, each one must generally beindividually configured to monitor a process variable. FIG. 4illustrates an example configuration display 84 that may be presented toa user, engineer, etc. to depict and change the current SPMconfiguration for a device. As indicated in the display 84, SPM blocks1, 2 and 3 for this particular device have all been configured, whileSPM block 4 has not been configured. Each of the configured SPM blocksSPM1, SPM2 and SPM3 is associated with a particular block within adevice (as indicated by the block tag), a block type, a parameter indexwithin the block (i.e., the parameter being monitored) and a usercommand which indicates the monitoring functionality of the SPM block.Still further, each configured SPM block includes a set of thresholds towhich determined statistical parameters are to be compared, includingfor example, a mean limit, a high variation limit (which specifies avalue that indicates too much variation in the signal) and low dynamics(which specifies a value that indicates too little variation in thesignal). Essentially, detecting a change in a mean may indicate that theprocess is drifting up or down, detecting a high variation may mean thatan element within the process is experiencing unexpected noise (such asthat caused by increased vibration) and detecting a low variation maymean that a process signal is getting filtered or that an element isgetting suspiciously quiet, like a stuck valve for example. Stillfurther, baseline values, such as a mean and a standard deviation may beset for each SPM block. These baseline values may be used to determinewhether limits have been met or exceeded within the device. SPM blocks 1and 3 of FIG. 4 are both active because they have received user commandsto start monitoring. On the other hand, SPM block 2 is inactive becauseit is in the Idle state. Also, in this example SPM capabilities areenabled for the entire device as indicated by the box 86 and are set tobe monitored or calculated every five minutes, as indicated by the box88. Of course, an authorized user could reconfigure the SPM blockswithin the device to monitor other blocks, such as other functionblocks, within the device, other parameters associated with these orother blocks within the device, as well as to have other thresholds,baseline values, etc.

While certain statistical monitoring blocks are illustrated in FIGS. 2and 4, it will be understood that other parameters could be monitored aswell or in addition. For example, the SPM blocks, or the ADBs discussedwith respect to FIG. 2 may calculate statistical parameters associatedwith a process and may trigger certain alerts, based on changes in thesevalues. By way of example, Fieldbus type SPM blocks may monitor processvariables and provide 15 different parameters associated with thatmonitoring. These parameters include Block Tag, Block Type, Mean,Standard Deviation, Mean Change, Standard Deviation Change, BaselineMean, Baseline Standard Deviation, High Variation Limit, Low DynamicsLimit, Mean Limit, Status, Parameter Index, Time Stamp and User Command.The two most useful parameters are currently considered to be the Meanand Standard Deviation. However, other SPM parameters that are oftenuseful are Baseline Mean, Baseline Standard Deviation, Mean Change,Standard Deviation Change, and Status. Of course, the SPM blocks coulddetermine any other desired statistical measures or parameters and couldprovide other parameters associated with a particular block to a user orrequesting application. Thus, SPM blocks are not limited to the onesdiscussed herein.

As will be understood, the parameters of the SPM blocks (SPM1-SPM4)within the field devices may be made available to an external client,such as to the workstation 74 through the bus or communication network76 and the controller 60. Additionally or in the alternative, theparameters and other information gathered by or generated by the SPMblocks (SPM1-SPM4) within the ADBs 80 and 82 may be made available tothe workstation 74 through, for example, an OPC server 89. Thisconnection may be a wireless connection, a hardwired connection, anintermittent connection (such as one that uses one or more handhelddevices) or any other desired communication connection using any desiredor appropriate communication protocol. Of course, any of thecommunication connections described herein may use an OPC communicationserver to integrate data received from different types of devices in acommon or consistent format.

Still further, it is possible to place SPM blocks in host devices, otherdevices other than field devices, or other field devices to performstatistical process monitoring outside of the device that collects orgenerates the raw data, such as the raw process variable data. Thus, forexample, the application 38 of FIG. 2 may include one or more SPM blockswhich collect raw process variable data via, for example, the OPC server89 and which calculate some statistical measure or parameter, such as amean, a standard deviation, etc. for that process variable data. Whilethese SPM blocks are not located in the device which collects the dataand, therefore, are generally not able to collect as much processvariable data to perform the statistical calculations due to thecommunication requirements for this data, these blocks are helpful indetermining statistical parameters for devices or process variablewithin devices that do not have or support SPM functionality.Additionally, available throughput of networks may increase over time astechnology improves, and SPM blocks not located in the device whichcollects the raw data may be able to collect more process variable datato perform the statistical calculations. Thus, it will be understood inthe discussion below, that any statistical measurements or parametersdescribed to be generated by SPM blocks, may be generated by SPM blockssuch as the SPM1-SPM4 blocks in the ADBs 80 and 82, or in SPM blockswithin a host or other devices including other field devices. Moreover,abnormal situation detection and other data processing may be performedusing the statistical measures in the field devices or other devices inwhich the SPM blocks are located, and thus detection based on thestatistical measures produced by the SPM blocks is not limited todetection performed in host devices, such as user interfaces.

Importantly, the maximum beneficial use of raw statistical data and thecalculation of various statistical measures based on this data asdescribed above is dependent in large part on the accuracy of the raw orcollected data in the first place. A number of data processing functionsor methods may be applied in the SPM blocks to increase the accuracy orusefulness of the raw data and/or to preprocess the raw data and developmore accurate or better statistical data in the SPM blocks. These dataprocessing functions may be applied to massage or process raw field dataprior to exposing the raw or processed data to other field devices andhost systems. Moreover, in some cases, these data processing functionsmay be used to provide diagnostics on the processed data or on the rawdata to generate alarms and/or warnings to users, other field devicesand host systems. The below described data processing functions andmethodologies are applicable to all communication protocols such asHART, Fieldbus, Profibus, etc. and are applicable to all field devicessuch as transmitters, controllers, actuators, etc.

As will be understood, performing statistical and digital signalprocessing within a field device provides the capability to operate onthe raw measurement data before any measurement and control relatedmodifications are made in the plant using the raw data. Therefore, thesignatures computed within a device are the best indicators of the stateof the sensing system, the mechanical equipment and the process in whichthe device is installed. For most communication systems, raw datacollected at a high sampling rate cannot be passed to a host system on aplant-wide basis due to bandwidth limitations of the communicationprotocols between field devices and the host system. Even if it becomespossible in the future, loading the networks with excessive raw datatransfers will adversely affect the other tasks on the networks formeasurement and control. Thus, it is proposed in the first instance toprovide one or more data processing methodologies described hereinwithin SPM blocks or modules within the field devices or other deviceswhich collect the raw data.

As noted above, FIG. 3 illustrates a basic SPM block for performingstatistical process monitoring calculations on raw data. As an example,the Rosemount 3051 transmitters use a simpler version of the block ofFIG. 3, where only the mean and the standard deviation are computed andare passed to a host system. However, it has been determined thatcalculating these values as well as the RMS value and Range informationof a signal does not necessarily yield healthy monitoring anddiagnostics information in all cases. In fact, it has been found that insome cases, better statistics may be determined by comparing theseparameters not only to their past baselines, but also to similarparameters evaluated on processed forms of the raw data input. Inparticular, additional information may be obtained by having the SPMblock calculate statistical measures of the raw data as well asstatistical measures of filtered or processed versions of the raw dataand then comparing these calculated statistical measures. As illustratedin FIG. 5 for example, an SPM module 100 may include two SPM blocks 90 aand 90 b and a signal processing block 102. Raw data may be processed asusual in the SPM block 90 a to produce various statistical measures(e.g., Min. Max, Range, Mean, RMS, Standard Deviation, etc.) on the rawdata. However, the raw data may also be processed in the signalprocessing block 102, which may filter the raw data, trim the raw datato remover outliers, etc. The processed raw data may then be provided tothe SPM block 90 b which determines one or more statistical measures onthe processed data. The raw data statistical measures and the processeddata statistical measures may then be compared to one another to detector determine information about the raw data. Moreover, one or both ofthe raw data statistical measures and the processed data statisticalmeasures may be used in subsequent processing to perform, for example,abnormal situation detection.

Thus, as will be understood, the signal processing block 102 of FIG. 5may implement various data processing techniques that are extremelyuseful in performing monitoring and diagnostics within a process plantthat using statistical process monitoring. The first of these techniquesis the capability to trim raw data, which is useful in detecting andthen eliminating spikes, outliers and bad data points so that these datapoints do not slew statistical parameters. Trimming could be performedbased on sorting and removing certain top and bottom percentages of thedata, as well as using thresholds based on the standard deviation orsome weighted moving average. Trimmed points may be removed from thedata sequence, or an interpolation may be performed to replace outlierdata with an estimate of what that data should be based on other datacollected prior to and/or after that data.

Moreover, the signal processing block 102 may perform one or moredifferent types of filtering to process the raw data. FIG. 6 illustratesa signal processing block 102 a which includes multiple filters toenable a user or the person configuring the system to select the desiredtype of filtering. In the block 102 a of FIG. 6, three digital filterswhich may be applied individually or in combination to achieve goodresults in many applications, as well as good performance in determiningaccurate statistical data, are illustrated as a low pass filter 104, ahigh pass filter 105, and a bandpass filter 106. Of course other typesand numbers of filters could be provided as well or instead of thoseillustrated in FIG. 6. Additionally, a no filter option or block 107simply passes data unprocessed through the block 102 a, while an offblock 108 blocks data through the block 102 a. During configuration ofthe block 102 a, a user may select the one or more filters 104-108 whichare to be used to filter the data in the processing block 102 a. Ofcourse, the filters may be implemented using any known or availabledigital signal processing techniques and may be specified or definedusing any known filter parameters, for example, the desired slope of thefilter, the pass and rejection frequencies of the filter, etc.

FIG. 7 illustrates another signal processing block 102 b that can beused to filter and/or trim raw data. The signal processing block 102 bincludes multiple standard filters (which may be for example, low pass,high pass and band pass filters) 110 as well as a custom filter 112.These options enable a user to select any of a number of differentdesired filter characteristics within the processing block 102 b. Datatrimming blocks 115 may be placed before and/or after each of thefilters 110 and 112 to perform data trimming in any of the mannersdiscussed above or using any known or available technique. As will beunderstood, the data processing block 102 b enables a user or operatorto select between one or more standard filters to filter (and trim) theraw data as well as a custom filter to filter (and trim) the raw data toproduce filtered (and trimmed) data. This configuration of a filteringand trimming data to be provided to an SPM block provides a strong andversatile technology that can be used in a broad spectrum of monitoringand diagnostics applications.

Of course, many different types of filters may be used in the SPMmodules and data processing blocks such as those of FIGS. 5-7. In oneembodiment, it is possible to isolate the noise portion of a signalusing one or more digital high pass IIR (infinite impulse response)filters or FIR (finite impulse response) filters. A typical FIR filterof order n has the following structure:

$y_{t} = {\sum\limits_{i = 0}^{n}\; {a_{i}*x_{t - i}}}$

where y is the filtered value, x is the current/previous measurement anda is the filter coefficient. As is known, these filters are designed tomatch certain frequency response criteria to match a desired filtertransfer function.

FIR filters are known and are currently used in, for example, a knownplugged line diagnostics algorithm provided in known Rosemounttransmitters and in the Rosemount AMS SNAP-ON products. In these cases,the FIR filter is in the form of a 16^(th) order FIR filter with thetransfer function illustrated in FIG. 8. In this figure, frequency isnormalized so that 1 is equal to the half the sampling rate which is 1Hz. Therefore, as illustrated in FIG. 8, the displayed filter will blockall parts of the signal from DC to about 1.1 Hz and will pass the partsfrom about 3.3 Hz to 11 Hz. The transition band is from about 1.1 Hz toabout 3.3 Hz. The primary purpose of this filter is to remove transientsfrom the signal so that it is possible to compute the standard deviationof the noise. However, this filter can not guarantee that all transientswill be removed because some transients will have faster components(i.e., falling with the pass band of the filter). Unfortunately, it isnot possible to design a transition band much higher than that shown inFIG. 8 using FIR techniques because such a transition band would filterprocess noise along with transients. Thus, in summary, such an FIRfilter will either pass some transients or filter out some noise. Inaddition, because the DC gain will not be zero, the mean of the filteredsignal will not reach zero, but will instead carry an offset, which isnot desirable. Furthermore, because this filter is a 16^(th) orderfilter, it requires many computations at every point, which increasesthe required processing power and/or decreases the ability to performthe filtering in real time, especially when using a high sampling rate.

Another filter, which may be for example implemented as the customfilter 112 of FIG. 7 and that can be advantageously used in an SPM blockor module for any purpose, for example to perform plugged linediagnostics and flame instability detection, is a simple differencefilter. This difference filter can be pre-applied to a data measurementsequence (e.g., prior to SPM block processing) to evaluate and eliminateor reduce the short term variation in the measurement sequence orsignal. In particular, this proposed difference filter, which again maybe used to remove trends/transients and to isolate the noise portion ofa signal, may be implemented, in one embodiment, as a first orderdifference filter defined as:

y _(t) =x _(t) −x _(t-1)

wherein:y_(t) is the filtered output at time t, andx_(t) is the raw data at time t.

Of course, higher order difference filters may be used as well orinstead. The frequency response or transfer function of this filter isillustrated in FIG. 9 and, as will be understood, this filtercontinuously promotes higher frequencies and continuously demotes lowerfrequencies. Because the frequency content of the trends and transientsin a signal are unknown, this filter is believed to have an optimalstructure for all possible trends in a signal. As an example of theapplication of this filter, FIG. 10 illustrates a pressure signal 120,composed of signal trend and some pressure noise, while FIG. 11illustrates the filtered signal 122 after application of the proposedfirst order difference filter described above (i.e., with the transferfunction shown in FIG. 9). It can be clearly seen from these resultsthat a difference filter can handle a variety of pressure conditionswith minimal computations.

The primary advantage of the difference filter described above is thatit removes intermediate and long term variations in a given signal, andthat it isolates the short term variation in the signal, which issometimes called the “process noise.” Another advantage of thisdifference filter is that it is a first order filter and requires onlyone subtraction per measurement point, as compared to 17 multiplicationsand 16 additions needed by the 16^(th) order FIR filter described above.This difference filter is therefore extremely computationally efficientand is thus well-suited for on-board applications, i.e., those providedwithin field devices and SPM blocks or modules located in the deviceswithin the process plant.

Another important aspect of making accurate and useful statisticaldeterminations in SPM blocks (and elsewhere) involves selecting anappropriate data block or time length over which to calculate thestatistical measures, such as the mean, the standard deviation, etc. Infact, an inherent problem in calculating the mean, standard deviation,etc. for a given data sequence, is that these statistical parametersdepend heavily on the length of the time period and thus the number ofdata points used to perform the calculations. Using pure statisticalguidelines for the number of points as an appropriate sample set oftendoes not work well because most processes do not fit the underlyingstatistical assumptions exactly, and thus the number of steady statepoints suggested by these guidelines may not be available at anyparticular time.

One method of calculating an appropriate block length to use, however,includes collecting, during a test period, a number of test points for asignal, wherein the number of test points is much greater than thepossible block length, determining the frequency components (e.g.,frequency domain) of the signal based on the collected test points,determining the dominant system time constant from the frequencycomponents and then setting the block length as some multiple (which maybe an integer or a non-integer multiple) of the dominant system timeconstant.

According to this method, the frequency components or domain of a signalX(t) is first determined. For example, assume that the data sequence inthe time domain is given by X(t)=x₁, x₂, x₃, . . . x_(n), wherein the xdata points are measured at times t₁, t₂, t₃, . . . t_(n). Here, it isassumed that the corresponding time points t are uniformly spaced. Thetime domain representation of a typical pressure signal 130 is depictedin FIG. 12. Next, a Fourier Transform, such as a Fast Fourier Transformmay be applied to the pressure signal 130 to determine the frequencycomponents of the pressure signal 130. An example transformed signalX(f) illustrating the frequency domain of X(t) for the pressure signal130 of FIG. 12 is illustrated as the plot 132 in FIG. 13. As is known,the FFT 132 of the signal X(t), illustrates all of the cyclic behaviorin the data as a function of cyclic frequencies.

Next, a corner frequency f_(c) of the pressure signal may be determinedby (1) finding the frequency where the FFT drops to some factor (such asa factor of 10) from its peak and (2) finding any isolated peaks in theFFT. In particular, it is desirable to eliminate isolated peaks in theFFT prior to determining the frequency drop because these peaks can pullthe maximum FFT values artificially high. That is, the corner frequencyshould be determined based on the drop from the low frequency level ofthe FFT after ignoring the isolated peaks or spikes in the FFT. Usingthe isolated peaks in the FFT might lead to errors in the cornerfrequency (or bandwidth) computations. Thus, in the plot of FIG. 13, thecorner frequency f_(c) may be selected as being approximately 10 Hz. Thecorner frequency f_(c) may then be used to develop or estimate thedominant system time constant T_(C). In one embodiment

T _(C)=1/f _(c).

A robust block size may then be chosen as some multiple of the dominantsystem time constant T_(c). For example, ten times the dominant systemtime constant T_(c) may be used to produce a robust block size for anyapplication. However, other integer or non-integer multiples of thedominant system time constant T_(c) may be used instead.

In some situations, it is desirable to fit or match a sine wave to aspecific data set to determine a best fit for a sine wave to the dataset, with the sine wave providing information about specifics of thedata set, such as dominant periodic frequency, etc. One method that maybe used to fit a sine wave to a given data set is through the use of alinear least squares technique. However, because the form of a sine waveis nonlinear, routine linear regression methods cannot be applied tofind the sine wave parameters, and thus nonlinear curve fittingtechniques have to be applied to evaluate the parameters. However,nonlinear curve fitting techniques typically require an excessive numberof iterative computations, which requires significant processing timeand power. Moreover, nonlinear techniques have to assure computationalstability and convergence to a solution, which are highly complexconcepts and hard to implement in SPM blocks or modules.

To overcome these problems, two practical manners of fitting a sine waveto a data set using a simple linear regression technique, but that canbe used in SPM blocks or other blocks within field devices withoutrequiring a lot of processing power are described below.

As is known, a generic sine wave may be expressed in the form of:

y(t)=a+b sin(ωt+φ)

and for this discussion, this will be the form of a sine wave to befitted. However, other sine wave forms may be used instead.

According to a first method of fitting this sine wave, referred toherein as a one pass fit method, the sine wave parameters a (the offset)and b (the gain) are first estimated using simple techniques. Forexample, the offset a may be estimated as the mean value of the entiredata set while the gain b may be estimated as half of the differencebetween a minimum and a maximum value of the entire data set. Of course,the offset a may be estimated using, for example, the median or otherstatistical measure and the gain b may be estimated using some othertechnique, such as using the root mean squared (RMS) value, etc.

Next, a variable transformation may be applied or selected as:

$z = \frac{{{Sin}^{- 1}(y)} - a}{b}$

where y is the measured data point. With this transformation, theregression expression (the original sine wave form becomes:

z(t)=ωt+φ

This equation is obviously in a linear form and, as a result, simplelinear regression expressions can be used to fit ω and φ as a functionof time, resulting in an estimate for each of the parameters of the sinewave (i.e., a, b, ω and φ. In particular, the variable transformationdefining z is used to compute the transformed data points z(t) for eachtime t. Then linear regression techniques can be used to select the ωand φ that best fit the set of data points z(t).

A second method, referred to herein as an iterative fit method, uses aniterative technique to determine the sine wave parameters of a, b, ω andφ. In this method, the initial values for a, b, ω and φ may be estimatedusing the technique of the one pass fit method described above. Next,the following variable transformation may be applied.

x=sin(ωt+φ)

With this transformation, the original sine wave expression (to be fit)becomes:

y(x)=a+bx.

This equation is in a linear form and therefore simple linear regressionexpressions can be used to fit a and b. These parameters may then beused along with the variable transformation defining x to fit for theparameters ω and φ. These iterations may be executed until one or allfour of the parameters (a, b, ω and φ) converge, that is where:

|a _(k) −a _(k-1)|<ε_(a)

|b _(k) −b _(k-1)|<ε_(b)

|ω_(k)−ω_(k-1)|<ε_(ω)

|φ_(k)−φ_(k-1)|<ε_(φ)

Where k is the iteration step and ε is the desired tolerance. The aboveconvergence criteria are absolute with respect to the parameters.However, if desired, a relative measure in percent may also be employedfor the parameters.

The first method outlined above provides an extremely fast one pass fitfor a function of sinusoidal shape using a linear least squares fit. Thesecond method combined with the first method, on the other hand, whilerequiring more calculations, typically provides a fit of the parametersto a desired accuracy with only a couple of iterations. However, bothmethods are extremely computationally efficient as compared to theirnonlinear counterparts, which results in significant savings inprocessing, memory and storage requirements, making these methods moresuitable for a variety of fitting applications within SPM blocks.

One advantageous manner of using an SPM block relates to the monitoringof a distillation column tray and performing diagnostics usingstatistical process monitoring for the distillation column tray. Inparticular, various diagnostics methodologies based on actual pressureand differential pressure readings can be used to determine the healthof distillation columns (also called fractionators). The distillationcolumn is probably one of the most important units in most refineriesand chemical plants, because the distillation column is responsible formost of the physical separation processes in these plants. Themethodologies described here could be implemented either in the fielddevices within the plant (in for example, a Rosemount 3426 transmitter),or at the host system as software. The main advantage of these methodsis the use of statistical process parameters that are evaluated by fieldinstruments but that provide high quality measurements and fasterestimates.

FIG. 14 illustrates a schematic of a typical distillation column 150found in many refineries or chemical plants. As can be see from FIG. 14,the distillation column 150 includes a fractionator 152 into which thefeed is applied. At the bottom of the fractionator 152, the heavy fluidor “bottoms” material is removed through a valve 154, which may becontrolled based on a level sensor 156 and a flow sensor or transmitter158. Some of the bottoms material is reheated in a reboiler 160 andprovided back into the fractionator 152 for further processing. At thetop of the fractionator 152, vapor is collected and is provided to acondenser 162 which condenses the vapor and supplies the condensedliquid to a reflux drum 164. Gas in the reflux drum 164 may be removedthrough a valve 166 based on a pressure sensor 168. Likewise, some ofthe condensed liquid in the reflux drum 164 is proved out as distillatethrough a valve 170 based on the measurements of a level sensor. In asimilar. manner, some of the condensed liquid in the reflux drum 164 isprovided back into the fractionator 152 through a valve 174 which may becontrolled using flow and temperature measurements from flow a sensor176 and a temperature sensor 178.

FIG. 15. illustrates a schematic of a typical fractionator 152 used inpetroleum processing showing the locations of various trays that aresometimes used to extract liquids at various physical condensationpoints. As illustrated in FIG. 15, flashed crude is injected at tray 5while heavy diesel is removed at tray 6, light diesel is removed at tray13 and kerosene is removed at tray 21. Preflashed gas and preflashedliquids may be injected at trays 27 and 30. While the followingdiscussion of the diagnostic methods used in the distillation columnrefers to the trays of FIG. 15 as, a baseline distillation columnconfiguration, these methods may be used in other distillation columnshaving other tray arrangements and structures.

The first processing method determines if there is a low pressure dropacross two trays of the column. In particular, if the pressure dropacross a tray is less than a low nominal pressure, it typically meansthat the tray is either damaged or is dumping. This nominal low pressure(P_(ln)) is, in one instance, 0.06 psi (pounds per square inch) for a 24inch diameter (D_(n)) distillation tray. For other sizes of traydiameters (D) the nominal low pressure P₁ may be calculated as:

$P_{l} = {P_{\ln}\sqrt{\frac{D}{D_{n}}}}$

Statistical process monitoring can be used to determine a baseline forthe pressure drop across a tray using any of the SPM blocks andtechniques described above, and then a monitoring phase may be used inan SPM or other block to detect the reduction in the mean pressure drop.If the differential pressure is measured across multiple trays, theexpected pressure drop is simply the pressure drop for a single traytimes the number of trays. Thus, after determining a baseline pressuredrop across a tray for the fractionator 152 of FIG. 15 using pressuresensors (not shown in FIG. 15) at the appropriate locations within thefractionator 152 or using a threshold established using the low nominalpressure calculations discussed above, SPM blocks may monitor thepressures to determine a mean pressure at each location and to determinethe difference between these mean pressures. If the difference becomeslower then the low nominal pressure (set as a threshold), then an alarmor alert may be sent indicating that the tray is damages or is dumping,or is at a condition that it will start this process.

Additionally, a high pressure drop across trays of a distillation columnmay be determined using this same technique. In particular, if thepressure drop across a tray is more than a high nominal pressure, ittypically indicates that either there is fouling or there is plugging(e.g., at least partial plugging) of the tray. The nominal high pressure(P_(hn),) may be 0.12 psi for a 24 inch diameter (D_(n)) distillationtray. For other sizes of trays, the P_(h) maybe calculated as:

$P_{h} = {P_{hn}\sqrt{\frac{D}{D_{n}}}}$

Similar to the low pressure drop method described above, statisticalprocess monitoring can be used to determine a baseline mean pressuredrop across a tray or a group of trays or a threshold may be establishedusing the calculations described above, and then the monitoring phase isused to detect the reduction in the mean pressure drop. If thedifferential pressure is measured across multiple trays, the expectedpressure drop is simply the pressure drop for a single tray times thenumber of trays. In either case, it will be understood that distillationcolumn pressure drop monitoring using statistical parameters provides afast and efficient indication of tray problems in chemical and refiningindustries.

Additionally, diagnostics using statistical process monitoring may beadvantageously performed in fluid catalytic crackers (FCCs). Inparticular, various diagnostic methodologies can be used to determinethe health of an FCC, which is highly advantageous because the FCC isprobably the most important unit in a refinery, as it is responsible formost of production of gasoline in a refinery, which is typically themost important and most prevalent product produced by the refinery. Thestatistical processing methodologies described here can be implementedeither in field devices, such as in the Rosemount 3420 transmitter, orat the host system as software. The main advantage of these methods isthe use of statistical process parameters evaluated by field instrumentsthat provide high quality measurements and faster estimates.

FIG. 16 illustrates a schematic of a typical FCC 200 found in refineriesand that will be used as the baseline FCC configuration for thediagnostic methods described herein. However, it will be understood thatthese methodologies may be used in other types of FCCs or in FCCs withother configurations as well. In particular, as illustrated in FIG. 16,the FCC 200 includes a reactor 202 and a catalyst regenerator 204.During operation, feed and dispersion steam are feed into a riser 206where the feed reacts with regenerated catalyst. This process “cracks”the feed. At the top of the reactor 202, the product and catalyst areseparated with the product being expelled as reactor effluent. Thecatalyst. falls to the bottom of the reactor 202 and is steam strippedusing stripping steam. The spent catalyst is then provided through apipe 206 controlled by a valve 208 to the regenerator 204. The spentcatalyst is input into a combustion chamber and is mixed withsuperheated air provided by an air blower 212 which burns the coke thathas formed on the catalyst as a result of the catalytic reaction in thereactor 202. This process regenerates the catalyst. The heat from thisprocess and the regenerated catalyst are then provided back to thebottom of the reactor 202 via a regenerated catalyst pipe 220 controlledby a regenerated catalyst valve 222 to mix with the incoming feed.

A first statistical method may be used in the FCC 200 to detect a failedor faulty air compressor or blower. In particular, a failed aircompressor results in a reversal of flow in the regenerated catalystpipe 220 resulting in flow from the reactor 202 to the regenerator 204.This condition may be detected by monitoring pressure in the regenerator204 or monitoring differential pressure across the regenerated catalystvalve 222. In particular, during normal operation of the FCC 200, thepressure in the regenerator 204 is higher than that in the reactor orriser pipe 202, which produces the flow of regenerated catalyst in thecorrect direction. Loss of the compressor 212 on the regenerator 204causes a loss of pressure at the regenerator 204 and results in areversal of this differential pressure.

Additionally, a statistical method may be used to detect reactor toregenerator pipe plugging. In particular, when the pipe 206 between thereactor 202 and the regenerator 204 plugs, the reactor 202 fills withcatalyst and the catalyst enters into the exhaust or reactor effluent.This condition may be detected by monitoring the mean catalyst level inthe reactor 202 using, for example, a level sensor/transmitter 224 asplugging in the pipe 202 causes the catalyst level in the reactor 202 torise. With proper catalyst level baselining, detecting the mean level ofthe catalyst within the reactor 202 and comparing it to a baseline meanlevel for the catalyst could be used to detect plugging in the pipe 206.A second indication that may be used to determine plugging of the pipe202 may be based on the cross correlation between the pressures andlevels in the reactor 202 and the regenerator 204, as the plugging ofthe pipe 206 would change this correlation. That is, a baseline crosscorrelation of the mean pressures and levels in the reactor 202 and theregenerator 206 may be determined and then a cross correlation betweenthese pressures and levels (or the means or other statistical measuresof these pressures and levels) may be periodically determined andcompared to the baseline, with a significant change in thecross-correlation indicating a potential plugging of the pipe 206.

Moreover, a statistical method may be used to detect a catalyst flowproblem or a flow instability in the reactor 202. In particular, acatalyst flow instability will result in a bad product quality and inthe catalyst entering into the exhaust of the reactor 202. Thiscondition may be detected using the standard deviation of thedifferential pressure across the regenerated catalyst valve 222, itbeing understood that a flow instability would cause an increase in thestandard deviation of the differential pressure across the catalystvalve 222.

A statistical method may also be used to detect if there is insufficientsteam flow into the reactor 202, which typically results in thermalcracking and coke formation. In particular, detecting insufficient steamflow and correcting the problem reduces catalytic cracking and givesrise to thermal cracking. The existence of insufficient steam flow canbe detected by monitoring the mean temperature in the reactor 202. Inparticular, an increase in mean the reactor temperature indicates ainsufficient steam flow problem.

A statistical method may also be used to detect an extreme thermaldistribution in the reactor 202, which leads to the formation of cokeand therefore fouling of the reactor 202. Extreme thermal distributionmay be detected by measuring the reactor temperature at multiple pointsin the reactor. Uneven temperatures would cause certain regions inreactor 202 to become very hot, which results in the formation of cokein the reactor. Monitoring these temperatures and detecting regions thathave very high or low temperatures (or very high or low meantemperatures) as compared to a baseline mean or a threshold yieldsdiagnostics related to extreme thermal distributions.

A statistical method may also be used to detect thermal cracking in theexhaust pipe after the reactor 202, which again leads to the formationof coke in this section of the FCC 200. This condition may be detectedby monitoring the mean temperature difference between the exhaust pipeand the reactor vessel. If the mean temperature difference becomes morethan some threshold level, such as three degrees Fahrenheit, there maybe thermal cracking occurring in the exhaust pipe.

There are three possible platforms to implement these statisticalmethods and detection. In particular, these conditions may be detectedas part of a transmitter advanced diagnostics block disposed within avalve or a transmitter within the FCC 200, such as in the valve 222, thevalve 208, a temperature sensor/transmitter, a level sensor/transmitter,a pressure sensor/transmitter, etc. In particular, this diagnostic blockmay be trained to detect or determine a baseline pressure, temperature,level, differential pressure, etc. when the system is healthy, and thenmay monitor the mean value of the appropriate pressures, temperatures,levels, differential pressures, etc. after establishing the baseline. Onthe other hand, this monitoring and detection could be achieved using anSPM block in a transmitter or other field device with a simple thresholdlogic. That is, the SPM block could monitor one or more processvariables to determine the mean, the standard deviation, etc. for thesevariables and compare these statistical measures to a pre-establishedthreshold (which may be set by a user or which may be based on abaseline statistical measure computed from measurements of theappropriate process variables during a training period). Also, ifdesired, host level software run in a user interface device or othercomputing device connected to the field devices, such as an advanceddiagnostic block explorer or expert, maybe used to set and monitornormal and abnormal pressures, temperatures, levels and differentialpressures and to perform abnormal situation detection based on theconcepts described above.

Some or all of the blocks, such as the SPM or ADB blocks illustrated anddescribed herein may be implemented in whole or in part using software,firmware, or hardware. Similarly, the example methods described hereinmay be implemented in whole or in part using software, firmware, orhardware. If implemented, at least in part, using a software program,the program may be configured for execution by a processor and may beembodied in software instructions stored on a tangible medium such asCD-ROM, a floppy disk, a hard drive, a digital versatile disk (DVD), ora memory associated with the processor. However, persons of ordinaryskill in the art will readily appreciate that the entire program orparts thereof could alternatively be executed by a device other than aprocessor, and/or embodied in firmware and/or dedicated hardware in awell known manner.

While the invention is susceptible to various modifications andalternative constructions, certain illustrative embodiments thereof havebeen shown in the drawings and are described in detail herein. It shouldbe understood, however, that there is no intention to limit thedisclosure to the specific forms disclosed, but on the contrary, theintention is to cover all modifications, alternative constructions andequivalents falling within the spirit and scope of the disclosure asdefined by the appended claims.

1. A method of detecting an abnormal situation associated with a processplant, comprising: receiving measured data pertaining to a processparameter sensed by at least one sensor device associated with theprocess plant; determining one or more statistical measures associatedwith the process parameter using the measured data; and using the one ormore statistical measures associated with the process parameter todetect an abnormal situation within the process plant.
 2. The method ofclaim 1, further including the processing the measured data to produceprocessed data and wherein determining the one or more statisticalmeasures associated with the process parameter includes determining theone or more statistical measures using the processed data.
 3. The methodof claim 1, further including determining a block length for use incomputing the one or more statistical measures from the measured data.4. The method of claim 3, wherein determining the block length includescollecting a number of first data points for the process parameter,determining a frequency component of the process parameter based on thecollected number of first data points, determining a dominant systemtime constant from the frequency component and setting the block lengthbased on the dominant system time constant.
 5. The method of claim 4,wherein determining the frequency component includes performing aFourier Transform on the collected number of first data points.
 6. Themethod of claim 4, wherein setting the block length includes selectingthe block length as a multiple of the dominant system time constant. 7.The method of claim 4, wherein determining the dominant system timeconstant includes determining a corner frequency from the frequencycomponent and determining the dominant system time constant as a factorof the corner frequency.
 8. The method of claim 7, wherein determiningthe corner frequency includes determining a first frequency componentwith a peak magnitude and determining a further frequency component atwhich the magnitude of the further frequency component drops to apredetermined factor below the peak magnitude of the first frequencycomponent.
 9. The method of claim 1, wherein determining the one or morestatistical measures includes fitting the measured data to a sine wave.10. The method of claim 9, wherein fitting the measured data to a sinewave includes determining first and second parameters of the sine wavebased on statistical measures of the process parameter determined fromthe measured data.
 11. The method of claim 10, wherein the firstparameter of the sine wave is an offset and the second parameter of thesine wave is a gain.
 12. The method of claim 10, wherein determining thefirst and second parameters of the sine wave includes determining theoffset as a mean value of the process parameter and determining the gainbased on the difference between a minimum value and a maximum value ofthe process parameter.
 13. The method of claim 10, including using avariable transformation of a mathematical expression of the sine wavethat produces a linear expression having third and fourth sine waveparameters associated therewith, producing a set of transformed datapoints based on the variable transformation, performing a linearregression to fit the transformed data points to the linear expressionand determining the third and fourth sine wave parameters based on thelinear regression.
 14. The method of claim 13, wherein the variabletransformation is of the form: $z = \frac{{{Sin}^{- 1}(y)} - a}{b}$wherein: z is a transformed data point; y is a measured data point; a isa sine wave offset parameter; and b is a sine wave gain parameter, andwherein the linear expression is of the form:z(t)=ωt+φ wherein: z(t) is the transformed data point at a time t; ω isa sine wave periodic frequency parameter; and φ is a sine wave phaseparameter.
 15. The method of claim 14, further including applying avariable transformation to produce a further linear expression includingthe sine wave offset and gain parameters, applying a linear regressionto the further linear expression to determine a new set of values forthe sine wave offset and gain parameters and determining a new set ofvalues for the sine wave periodic frequency and phase parameters basedon the new set of values for the sine wave off set and gain parameters.16. The method of claim 15, including iteratively determining values forthe sine wave offset, gain, periodic frequency and phase parametersuntil a change in the values for one or more of the sine wave offset,gain, periodic frequency and gain parameters becomes less than athreshold value.
 17. The method of claim 1, wherein determining the oneor more statistical measures associated with the process parameterincludes determining a baseline value of a first statistical measure ofthe process parameter and determining a further statistical measure ofthe process parameter from the measured data, and wherein using the oneor more statistical measures associated with the process parameter todetect an abnormal situation within the process plant includes comparingthe baseline value of the first statistical measure of the processparameter to the further statistical measure of the process parameter todetermine the existence of an abnormal situation.
 18. The method ofclaim 17, wherein determining the baseline value of the firststatistical measure of the process parameter includes determining thebaseline value as a statistical measure of a first set of the measureddata, and wherein determining a further statistical measure of theprocess parameter from the measured data includes determining thefurther statistical measure of the process parameter from a second setof the measured data.
 19. The method of claim 17, wherein determiningthe baseline value of the first statistical measure of the processparameter includes using a predetermined value of the process parameteras the baseline value of the first statistical measure of the processparameter.
 20. The method of claim 17, wherein the process parameter isa differential pressure between two locations in the process plant. 21.The method of claim 20, wherein the differential pressure is adifferential pressure between two trays of a distillation column. 22.The method of claim 21, wherein the differential pressure is adifferential pressure between two adjacent trays of a distillationcolumn.
 23. The method of claim 21, wherein the differential pressure isa differential pressure between two non-adjacent trays of a distillationcolumn.
 24. The method of claim 21, wherein the baseline value of thefirst statistical measure of the process parameter is a low differentialpressure value and wherein comparing the baseline value of the firststatistical measure of the process parameter to the further statisticalmeasure of the process parameter to determine the existence of anabnormal situation includes detecting tray dumping or tray damage whenthe further statistical measure of the process parameter is less thanthe low differential pressure value.
 25. The method of claim 21, whereinthe baseline value of the first statistical measure of the processparameter is a high differential pressure value and wherein comparingthe baseline value of the first statistical measure of the processparameter to the further statistical measure of the process parameter todetermine the existence of an abnormal situation includes detecting trayplugging when the further statistical measure is greater than the highdifferential pressure value.
 26. The method of claim 20, wherein theprocess parameter is a differential pressure across a catalyst valve ina fluid catalytic cracker and wherein comparing the baseline value ofthe first statistical measure of the process parameter to the furtherstatistical measure of the process parameter to determine the existenceof an abnormal situation includes detecting an air blower problem whenthe mean value of the differential pressure across the catalyst valve isless than the baseline value.
 27. The method of claim 20, wherein theprocess parameter is a differential pressure across a catalyst valve ina fluid catalytic cracker, and wherein comparing the baseline value ofthe first statistical measure of the process parameter to the furtherstatistical measure of the process parameter to determine the existenceof an abnormal situation includes detecting a catalyst flow problem whenthe standard deviation of the differential pressure across the catalystvalve is greater than the baseline value.
 28. The method of claim 20,wherein the process parameter is a differential pressure between acatalyst regenerator and a reactor in a fluid catalytic cracker andwherein comparing the baseline value of the first statistical measure ofthe process parameter to the further statistical measure of the processparameter to determine the existence of an abnormal situation includesdetecting an air flow malfunction when the differential pressure betweenthe catalyst regenerator and the reactor in the fluid catalytic crackeris less than the baseline value.
 29. The method of claim 17, wherein theprocess parameter is a level parameter.
 30. The method of claim 29,wherein comparing the baseline value of the first statistical measure ofthe process parameter to the further statistical measure of the processparameter to determine the existence of an abnormal situation includesdetecting pipe plugging when the further statistical measure of thelevel parameter becomes greater than the baseline value.
 31. The methodof claim 17, wherein the process parameter includes first and secondlevel parameters and first and second pressure parameters and whereinthe further statistical measure of the process parameter is a crosscorrelation between the first and second level parameters and the firstand second pressure parameters and wherein comparing the baseline valueof the first statistical measure of the process parameter to the furtherstatistical measure of the process parameter to determine the existenceof an abnormal situation includes detecting plugging when the crosscorrelation between the first and second level parameters and the firstand second pressure parameters exceeds the baseline value.
 32. Themethod of claim 17, wherein the process parameter is a temperatureparameter.
 33. The method of claim 32, wherein the temperature parameteris a temperature in a reactor of a fluid catalytic cracker and whereincomparing the baseline value of the first statistical measure of theprocess parameter to the further statistical measure of the processparameter to determine the existence of an abnormal situation includesdetecting insufficient steam flow when the statistical measure of thetemperature in the reactor becomes greater than the baseline value. 34.The method of claim 33, wherein the statistical measure of thetemperature in the reactor is a mean value of the temperature in thereactor.
 35. The method of claim 32, wherein the temperature parameteris a temperature in a reactor of a fluid catalytic cracker and whereincomparing the baseline value of the first statistical measure of theprocess parameter to the further statistical measure of the processparameter to determine the existence of an abnormal situation includesdetecting thermal extremes when the statistical measure of thetemperature in the reactor becomes greater than a first baseline valueor less than a second baseline value.
 36. The method of claim 17,wherein the process parameter is a differential temperature between twolocations of the process plant.
 37. The method of claim 36, wherein theprocess parameter is a differential temperature between two locations ofa fluid catalytic cracker and wherein comparing the baseline value ofthe first statistical measure of the process parameter to the furtherstatistical measure of the process parameter to determine the existenceof an abnormal situation includes detecting thermal cracking when thefurther statistical measure of the differential temperature exceeds thethreshold.
 38. The method of claim 37, wherein the process parameter isa differential temperature between a reactor and an exhaust pipe of thereactor within the fluid catalytic cracker.
 39. A method of detecting anabnormal situation in a fluid catalytic cracker, comprising: receivingmeasurements of a process parameter in the fluid catalytic cracker;determining a statistical measure of the process parameter from theprocess parameter measurements; comparing the statistical measure of theprocess parameter to a baseline value; and detecting the existence of anabnormal situation based on the comparison of the statistical measure ofthe process parameter to the baseline value.
 40. The method of claim 39,further including determining the baseline value as a predeterminedvalue.
 41. The method of claim 39, further including determining thebaseline value as a statistical measure of a first set of themeasurements of the process parameter.
 42. The method of claim 39,wherein the process parameter is a differential pressure between twolocations in the fluid catalytic cracker and wherein the statisticalmeasure of the process parameter is a mean of the differential pressurebetween two locations in the fluid catalytic cracker.
 43. The method ofclaim 39, wherein the process parameter is a differential pressureacross a catalyst valve in the fluid catalytic cracker, wherein thestatistical measure of the process parameter is a mean of thedifferential pressure across the catalyst valve in the fluid catalyticcracker and wherein detecting the existence of an abnormal situationbased on the comparison of the statistical measure of the processparameter to the baseline value includes detecting an air blower problemwhen the mean value of the differential pressure across the catalystvalve is less than the baseline value.
 44. The method of claim 39,wherein the process parameter is a differential pressure across acatalyst valve in the fluid catalytic cracker, wherein the statisticalmeasure of the process parameter is a standard deviation of thedifferential pressure across the catalyst valve in the fluid catalyticcracker and wherein detecting the existence of an abnormal situationbased on the comparison of the statistical measure of the processparameter to the baseline value includes detecting a catalyst flowproblem when the standard deviation of the differential pressure acrossthe catalyst valve is greater than the baseline value.
 45. The method ofclaim 39, wherein the process parameter is a level parameter within thefluid catalytic cracker, wherein the statistical measure of the processparameter is a mean of the level parameter and wherein detecting theexistence of an abnormal situation based on the comparison of thestatistical measure of the process parameter to the baseline valueincludes detecting pipe plugging when the mean of the level parameterbecomes greater than the baseline value.
 46. The method of claim 39,wherein the process parameter includes a first level parameter and afirst pressure parameter in a reactor of the fluid catalytic cracker andincludes a second level parameter and a second pressure parameter in aregenerator of the fluid catalytic cracker, wherein the statisticalmeasure of the process parameter is a cross correlation between thefirst and second level parameters and the first and second pressureparameters, and wherein detecting the existence of an abnormal situationbased on the comparison of the statistical measure of the processparameter to the baseline value includes detecting pipe plugging betweenthe reactor and the regenerator when the cross correlation changes by avalue greater than the baseline value.
 47. The method. of claim 39,wherein the process parameter is a temperature parameter within thefluid catalytic cracker, wherein the statistical measure of the processparameter is a mean of the temperature parameter and wherein detectingthe existence of an abnormal situation based on the comparison of thestatistical measure of the process parameter to the baseline valueincludes detecting insufficient steam flow when the mean of thetemperature in the fluid catalytic cracker becomes greater than thebaseline value.
 48. The method of claim 39, wherein the processparameter is a temperature parameter within the fluid catalytic cracker,wherein the statistical measure of the process parameter is a mean ofthe temperature parameter and wherein detecting the existence of anabnormal situation based on the comparison of the statistical measure ofthe process parameter to the baseline value includes detecting thermalextremes when the statistical measure of the temperature in the fluidcatalytic cracker becomes greater than a first baseline value or lessthan a second baseline value.
 49. The method of claim 39, wherein theprocess parameter is a differential temperature within the fluidcatalytic cracker, wherein the statistical measure of the processparameter is a mean of the differential temperature and whereindetecting the existence of an abnormal situation based on the comparisonof the statistical measure of the process parameter to the baselinevalue includes detecting thermal cracking when mean of the differentialtemperature exceeds the baseline value.
 50. The method of claim 39,wherein determining the statistical measure of the process parameterfrom the process parameter measurements, comparing the statisticalmeasure of the process parameter to the baseline value and detecting theexistence of the abnormal situation are performed within a field devicethat detects the measurements of the process parameter.
 51. A method ofdetecting an abnormal situation in a distillation column, comprising:receiving measurements of a process parameter in the distillationcolumn; determining a statistical measure of the process parameter fromthe process parameter measurements; comparing the statistical measure ofthe process parameter to a baseline value; and detecting the existenceof an abnormal situation based on the comparison of the statisticalmeasure of the process parameter to the baseline value.
 52. The methodof claim 51, wherein the differential pressure is a differentialpressure between two trays of the distillation column.
 53. The method ofclaim 52, wherein the differential pressure is a differential pressurebetween two adjacent trays of the distillation column.
 54. The method ofclaim 52, wherein the baseline value is a low differential pressurevalue, the statistical measure of the process parameter is a mean of thedifferential pressure and wherein detecting the existence of an abnormalsituation includes detecting tray dumping or tray damage when the meanof the differential pressure is less than the low differential pressurevalue.
 55. The method of claim 52, wherein the baseline value is a highdifferential pressure value, the statistical measure of the processparameter is a mean of the differential pressure and wherein detectingthe existence of an abnormal situation includes detecting tray pluggingwhen the mean of the differential pressure is greater than the highdifferential pressure value.
 56. The method of claim 52, whereindetermining the statistical measure of the process parameter from theprocess parameter measurements, comparing the statistical measure of theprocess parameter to the baseline value and detecting the existence ofthe abnormal situation are performed within a field device that detectsthe measurements of the process parameter.
 57. A method of processingdata collected in a process plant, comprising: using a first set of thecollected data points to determine a block length for calculating one ormore statistical measures of the collected data including; determining afrequency component of the first set of the collected data points,determining a dominant system time constant from the frequencycomponent; and setting the block length based on the dominant systemtime constant; and using the block length to determine a number of datapoints to use in calculating the one or more statistical measures of thecollected data.
 58. The method of claim 57, wherein determining thefrequency component includes performing a Fourier Transform on the firstset of collected data points.
 59. The method of claim 57, whereinsetting the block length includes selecting the block length as amultiple of the dominant system time constant.
 60. The method of claim57, wherein determining the dominant system time constant includesdetermining a corner frequency from the frequency component anddetermining the dominant system time constant as a factor of the cornerfrequency.
 61. The method of claim 57, wherein using the first set ofthe collected data points to determine the block length and using theblock length to determine the number of data points to use incalculating the one or more statistical measures of the collected dataare performed within a field device that performs measurements toproduce the data collected in the process plant.
 62. A method of fittinga sine wave to data collected within a process plant, comprising:determining a first set of parameters of the sine wave based on one ormore statistical measures of the process parameter determined from thedata collected within the process plant; storing a variabletransformation of a mathematical expression of the sine wave thatproduces a linear expression having a second set of sine wave parametersassociated therewith; using the variable transformation to produce a setof transformed data points from the data collected within the processplant; performing a linear regression to fit the transformed data pointsto the linear expression; and determining the second set of sine waveparameters based on the linear regression.
 63. The method of claim 62,wherein the first set of parameters of the sine wave includes an offsetand a gain.
 64. The method of claim 63, wherein determining the firstset of parameters of the sine wave includes determining the offset as amean value of the data collected within the process plant anddetermining the gain based on the difference between a minimum value anda maximum value of the data collected within the process plant.
 65. Themethod of claim 63, wherein the second set of parameters of the sinewave includes a cyclic frequency and a phase.
 66. The method of claim63, wherein the variable transformation is of the form:$z = \frac{{{Sin}^{- 1}(y)} - a}{b}$ wherein: z is a transformed datapoint; y is a collected data point; a is the offset; and b is the gain,and wherein the linear expression is of the form:z(t)=ωt+φ wherein: z(t) is the transformed data point at a time t; ω isa periodic frequency; and φ is a phase.
 67. The method of claim 66,further including applying a variable transformation to produce afurther linear expression including the offset and the gain, applying alinear regression to the further linear expression to determine a newset of values for the offset and the gain and determining a new set ofvalues for the periodic frequency and the phase based on the new set ofvalues for the offset and the gain.
 68. The method of claim 67,including iteratively determining values for the sine wave offset, gain,periodic frequency and phase until a change in the values for one ormore of the sine wave offset, gain, periodic frequency and phase becomesless than one or more threshold values.
 69. The method of claim 62,wherein determining the first set of parameters of the sine wave, usingthe variable transformation, performing the linear regression anddetermining the second set of sine wave parameters are performed in adevice that collects or measures the data collected within the processplant.